Determine limit `lim_(x->oo) ((cos (1/x))^x)^2`

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justaguide eNotes educator| Certified Educator

The limit `lim_(x->oo) ((cos (1/x))^x)^2` has to be determined.

`lim_(x->oo) ((cos (1/x))^x)^2`

`x -> oo => 1/x -> 0`

`lim_(x->oo) ((cos (1/x))^x)^2`

= `((cos 0)^oo)^2`

= `1^2`

= 1

The limit `lim_(x->oo) ((cos (1/x))^x)^2 = 1`

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